@Georgiy Shvartsberg The issue is about the Live ID/Microsoft account restore, not specific to Azure. Ref: https://support.microsoft.com/en-us/account-billing/help-with-the-microsoft-account-recovery-form-b19c02d1-a782-dee6-93c3-dc8113b20c42
You could probably raise a support case to get some alternate option. For example: Adding another account as Co-Admin to the subscription, that way you you do not have to wait till 12/16.
Here is the link - https://learn.microsoft.com/en-us/azure/azure-portal/supportability/how-to-create-azure-support-request to create support case. Please create a support ticket to Azure subscription management team.